Kubiak said the surgery will take place "sometime quickly in the next week."
Leinart was injured in Sunday's win at Jacksonville when he landed on his shoulder after taking a hit from Jaguars defensive end Jeremy Mincey late in the second quarter.
Rookie T.J Yates came in for Leinart, leading Houston to the 20-13 win, and appears to be the new starter at least for the time being.
Former Jets quarterback Kellen Clemens is also on the roster, signed last week when Schaub was placed on IR.
Kubiak said he is focused on moving forward with Yates and Clemens, but the team is also exploring other options. Jeff Garcia and Brodie Croyle are among the free agents who have worked out for the AFC South leaders.
"We will bring another guy in," said Kubiak. "When that will happen, I don't know."
The coach declined to rule out Brett Favre when asked to do so. The retired quarterback, so often rumored to fill high-profile vacancies, played the last two seasons with Minnesota.
"I don't think you rule out anybody," said Kubiak. "I know there are a lot of guys being mentioned. I'm not going to rule out anybody nor confirm anybody."
He said Yates was in line for a "tall task" as the current starter, but that the team would rally around him. The 8-3 Texans, who have won five straight, host Atlanta on Sunday.
"I've got some issues on my hands, but I'm not down," said Kubiak. "This team is not down. I want the city to know that."